Nearly abelian, nilpotent, and Engel lattice-ordered groups

Rok, strany: 1995, 189 - 200

An $\ell$-variety is a class of lattice-ordered groups in which every substitution of elements into the variables of a set of words in the signature of $\{{}^*, {}^-1, e\}$ of groups, and $\{\wedge, \vee\}$ of lattices produces the identity element of the group. In this paper, we examine those classes of lattice-ordered groups in which every substitution produces a group element comparable to the group identity, and, under certain natural conditions, obtain a description of the structure of such lattice-ordered groups in terms of the radical of the corresponding $\ell$-variety. We especially concentrate on those sets of words which produce the $\ell$-varieties of abelian, nilpotent, Engel, and solvable lattice-ordered groups.

ISO 690:

Darnel, M., Wojciechowski, P. 1995. Nearly abelian, nilpotent, and Engel lattice-ordered groups. In Tatra Mountains Mathematical Publications, vol. 5, no.1, pp. 189-200. 1210-3195.

APA:

Darnel, M., Wojciechowski, P. (1995). Nearly abelian, nilpotent, and Engel lattice-ordered groups. Tatra Mountains Mathematical Publications, 5(1), 189-200. 1210-3195.